Problem: Divide the following complex numbers: $\dfrac{10 e^{4\pi i / 3}}{ e^{\pi i / 2}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $10 e^{4\pi i / 3}$ ) has angle $\frac{4}{3}\pi$ and radius 10. The second number ( $ e^{\pi i / 2}$ ) has angle $\frac{1}{2}\pi$ and radius 1. The radius of the result will be $\frac{10}{1}$ , which is 10. The angle of the result is $\frac{4}{3}\pi - \frac{1}{2}\pi = \frac{5}{6}\pi$ The radius of the result is $10$ and the angle of the result is $\frac{5}{6}\pi$.